Given log(a) and log(b) calculate log(a + b) boils down to log( exp(log_a) + exp(log_b) ) but this might overflow, so we turn this into log([exp(log_a - log_c) + exp(log_b - log_c)]exp(log_c)) and we set log_c == max(log_a,log_b) and so it becomes: LARGE + log(1 + exp(SMALL - LARGE)) == LARGE + log(1 + SMALL) ~= large the whole idea being to avoid an overflow (exp(LARGE) == VERY LARGE == overflow) - Java java.lang

Java examples for java.lang:Math Calculation

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Description

Given log(a) and log(b) calculate log(a + b) boils down to log( exp(log_a) + exp(log_b) ) but this might overflow, so we turn this into log([exp(log_a - log_c) + exp(log_b - log_c)]exp(log_c)) and we set log_c == max(log_a,log_b) and so it becomes: LARGE + log(1 + exp(SMALL - LARGE)) == LARGE + log(1 + SMALL) ~= large the whole idea being to avoid an overflow (exp(LARGE) == VERY LARGE == overflow)

Demo Code

/**/*from w  ww .ja v  a 2  s. co  m*/
 * Copyright (c) 2011, The University of Southampton and the individual contributors.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without modification,
 * are permitted provided that the following conditions are met:
 *
 *   *    Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 *
 *   *   Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 *
 *   *   Neither the name of the University of Southampton nor the names of its
 *    contributors may be used to endorse or promote products derived from this
 *    software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
//package com.java2s;

public class Main {
    /**
     * Given log(a) and log(b) calculate log(a + b) boils down to log(
     * exp(log_a) + exp(log_b) ) but this might overflow, so we turn this into
     * log([exp(log_a - log_c) + exp(log_b - log_c)]exp(log_c)) and we set log_c
     * == max(log_a,log_b) and so it becomes: LARGE + log(1 + exp(SMALL -
     * LARGE)) == LARGE + log(1 + SMALL) ~= large the whole idea being to avoid
     * an overflow (exp(LARGE) == VERY LARGE == overflow)
     *
     * @param log_a
     * @param log_b
     * @return log(a+b)
     */
    public static double logSum(final double log_a, final double log_b) {
        double v;

        if (log_a < log_b) {
            v = log_b + Math.log(1 + Math.exp(log_a - log_b));
        } else {
            v = log_a + Math.log(1 + Math.exp(log_b - log_a));
        }
        return (v);
    }
}

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